Conway — The Djjnamics of a Rigid Electron. 171 



to them from the origin pi, p. . . . . The forces on each particle Ws are 

 threefold, a mechanical force E, of electrical origin due to the magnitude, 

 position, and motion of the other electrical charges, a force §/ due to the 

 reactions of the rigid connexions, and a force |/' due to external causes. 

 The equation of motion is 



By operating with Vps ( ) we get the equation of moments with 

 respect to the origin 



msVp.sps= ^ps^s+ Vpsh' + Vps^s". 



By summing these equations for all the particles of the rigid system we 

 get the two vector equations of motion of the rigid body. By D'Alembert's 

 principle 2|/ = 0, S Vp.^s = 0, so that we get 



^ms-ps = S?. + Sr, (1) 



2m, Vps-ps = 2 Vps^s + S Fp|/^ - (2) 



If we consider mi = niz = etc. = 0, the equations may be written 



- S?, = X'': (3) 



-^VpsKs = i/', (4) 



where A'' and p." are the external force and couple. These equations 

 would be suitable for a theory which would regard all mass as of electrical 

 origin. 



In unobstructed aether the electric force c and the magnetic force r? 

 are connected by the equations 



v-'t = FV,7, 

 -7)= FVf. 



where u is the velocity of light. The vectors £ and tj can be conveniently 

 expressed in terms of a scalar potential j?, and a vector potential ct thus, 



pr^e = - VjJ - ra, 



where u~^p = SVzj. 



The mechanical force exerted on a charge e (in electromagnetic units) situated 

 at the end of the vector p is 



ee + eVpt] = eu-{- Vp - -^ + Vp FV?^). 



A charge e, at the end of the vector p^ will produce at a time t and 

 at the end of the vector p a field due to the position of pi at a previous 



[2+*] 



